The New South Glasgow Campus, which is the biggest hospital project in Europe, was scheduled for completion on February 15 2015.
However, speaking at the Govan site, Health Secretary Alex Neil announced that progress has allowed NHS chiefs to move this date forward to January 2015.
Mr Neil also unveiled the Government's White Paper on Health, in which he has pledged to do more to tackle health inequalities in Scotland should the country vote for independence.
The first patients are expected to be admitted to the new hospital in April, from the old Southern General, when staff will also transfer.
Inpatient beds will then be transferred from the old Victoria Infirmary, the Western and finally Yorkhill Children's Hospital, which will all close.
A number of services from other hospitals, including the Royal Alexandra Hospital, in Paisley, will also transfer to the new Southern.
At its peak, around 15,500 workers have been employed on the hospital project.
Mr Neil also confirmed that a £20m admin support building, which was included in the budget, will go ahead as planned because the project is on budget.
The building will house 1200 clinical and admin staff transferring from other hospitals.
The Health Secretary warned that welfare reforms introduced by Westminster could cost Scotland £100m a year, as he unveiled Scotland's Future and Scotland's Health, which pledges to protect free prescriptions, elderly care and invest more money in tackling health inequalities.
Children born in the poorest parts of the country can still expect to live 11 years less than those living in the wealthiest areas.
He said: "Life expectancy should not be decided on where you are born - independence will give us the levers and opportunity to end generations of failure on this issue from Westminster.
"The superb flagship project to build a new South Glasgow Hospital is apt demonstration of the Government's commitment to and investment in Scotland's NHS."
He said a new £20m Centre for Stratified Medicine, which is also being built on the Southern site to develop personalised treatments for diseases such as cancer, would reinforce the city's reputation as a world leader in health care.
Health chiefs say the new hospital will represent the "gold standard" of healthcare, with adult acute services, maternity and a children's hospital all on one site.